Anomalous thermal expansion in $\alpha$-titanium

TL;DR

This paper provides a comprehensive theoretical explanation for the anisotropic thermal expansion of hcp titanium, highlighting the negative expansion along the c-axis at low temperatures due to electronic and phononic effects.

Contribution

It introduces a parameter-free theory that accurately predicts the negative thermal expansion in titanium, identifying a Van Hove singularity as the key factor.

Findings

Negative thermal expansion along the c-axis below 170 K

Theoretical predictions match experimental observations

Van Hove singularity near the Fermi level influences expansion

Abstract

We provide a complete quantitative explanation for the anisotropic thermal expansion of hcp Ti at low temperature. The observed negative thermal expansion along the c-axis is reproduced theoretically by means of a parameter free theory which involves both the electron and phonon contributions to the free energy. The thermal expansion of titanium is calculated and found to be negative along the c-axis for temperatures below $\sim$ 170 K, in good agreement with observations. We have identified a saddle-point Van Hove singularity near the Fermi level as the main reason for the anisotropic thermal expansion in $\alpha-$titanium.